Question concerning credit card dispute against my business?

Sorry if this is too much info. Just wanted to be sure that I cover everything.

During the fall and winter I run an online children’s boutique. We specialize in higher end children’s items and mostly pettiskirts. I was contacted in January by someone wanting to place a 0 order for skirts going from the states to Singapore. The items were paid for through Paypal and drop shipped to the buyer by the skirt manufacturer. I placed an order, with the manufacturer, for my own children and did so for several other customers as well. All have confirmed that they received their skirts within a week. I am now, more than 5 months later, being contacted by the Singapore buyer who claims she never received hers. Again, more than 5 months later!!! She attempted filing with Paypal but they immediately closed the claim due to it being so long after purchase. However, they did mention that she could file directly with her credit card company and could still be refunded!!! I am so upset. I do not run my boutique through Summer months in order to spend time with my children when they are not in school. Each summer I delete all of my order information, emails, files, etc., so I can get a fresh start the next fall. This has kept things more organized for me up until now. Due to it being so long without hearing from anyone, I no longer have the shipping information. The only thing that I have is the email in which I sent when the order was shipped in January 14th. So now to the question…….Can she really get her money back after this long? In my opinion she should not be able to because there is no reason why she should not have contacted me earlier if she did not receive her order. Infact, I had told her only it would only take a couple of weeks when she first contacted me. I am wondering if she is trying to scam "me" considering the situation and the fact that she is from another country. At this point I no longer have the profit that I made on the skirts to refund her. I am a stay at home mom and with the site being closed through the summer, I have no extra money myself. What can I do? Any information on this or advise would be greatly appreciated!!!
Just to follow up with MEG D….. As I mentioned, I no longer have record of anything except for the email in my sent folder confirming to her that the order had shipped. The skirt was drop shipped direct from the manufacturer and they no longer have the information after this long. We are talking 1/2 a year later! They do have the order sheet where it was highlighted when the package was on the shipping table and another sheet that was highlighted once it was on the truck. So it definitely went out. They also print labels direct rather than retyping them or hand writing them so no error with the address. Hopefully you are right about the card company. I honestly do not have the money to loose with this. Thanks so much for your time!!